Problem: Graph this system of equations and solve. $10x-y = 5$ $8x-2y = -2$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$ $\llap{-}2$ $\llap{-}3$ $\llap{-}4$ $\llap{-}5$ $\llap{-}6$ $\llap{-}7$ $\llap{-}8$ $\llap{-}9$ $\llap{-}10$ Click and drag the points to move the lines.
Answer: Convert the first equation, $10x-y = 5$ , to slope-intercept form. $y = 10 x - 5$ The y-intercept for the first equation is $-5$ , so the first line must pass through the point $(0, -5)$ The slope for the first equation is $10$ . Remember that the slope tells you rise over run. So in this case for every $10$ positions you move up $1$ position to the right. $10$ positions up from $(0, -5)$ is $(1, 5)$ Graph the blue line so it passes through $(0, -5)$ and $(1, 5)$ Convert the second equation, $8x-2y = -2$ , to slope-intercept form. $y = 4 x + 1$ The y-intercept for the second equation is $1$ , so the second line must pass through the point $(0, 1)$ The slope for the second equation is $4$ . Remember that the slope tells you rise over run. So in this case for every $4$ positions you move up $1$ position to the right. $4$ positions up from $(0, 1)$ is $(1, 5)$ Graph the green line so it passes through $(0, 1)$ and $(1, 5)$ The solution is the point where the two lines intersect. The lines intersect at $(1, 5)$.